Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower-lq-tree estimate and let T be a bounded linear operator from X which satisfies an upper-lp-tree estimate. Then T factors through a subspace of ( ∑ Fn)lr , where (Fn) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an (lp, lq) FDD. Similarly, let...

Let L(ν)⊗̂γqY = Lq(ν, Y ) and X⊗̂∆pL(μ) = Lp(μ,X). It is shown that any Lp(μ)-valued measure has finite L2(ν)-semivariation with respect to the tensor norm L(ν)⊗̂∆pL(μ) for 1 ≤ p < ∞ and finite Lq(ν)semivariation with respect to the tensor norm L(ν)⊗̂γqL(μ) whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor no...

Given two Banach spaces X and Y , we write L(X, Y ) for the space of all continuous linear operators from X to Y . A linear subspace J of L(X, Y ) is said to be an ideal if ATB ∈ J whenever A ∈ L(Y ), T ∈ J , and B ∈ L(X). It is known (see, e.g., Caradus:74 [CPY74]) that the only norm closed ideal in L(lp), 1 6 p < ∞ is the ideal of compact operators. The structure of closed ideals in L(lp ⊕ lq...

n this article, we prove an lp-lq-version of morgan’s theorem for the generalized bessel transform.

n this article, we prove An Lp-Lq-version of Morgan’s theorem for the generalized Bessel transform.

This paper proposes the design of linear quadratic (LQ) digital controller in Ball & Plate model in experimental environment. The non-linear mathematical model of Ball & Plate structure is presented and adequately linearized. Polynomial approach to controller design for two degrees of freedom (2DOF) controller structure is introduced as the main tool for determination of unknown parameters. Thi...

In our previous study we used the linear-quadratic model [J. Nucl. Med. 35, 1861 (1994)] to confirm our initial finding, based on the time-dose-fractionation model [J. Nucl. Med. 34, 1801 (1993)], that longer-lived radionuclides (e.g., 32P, 91Y) can offer a substantial therapeutic advantage over the shorter-lived radionuclides presently used in radioimmunotherapy (e.g., 90Y). The original calcu...

We consider a general class of nonlinear optimal policy problems involving forward-looking constraints (such as the Euler equations that are typically present as structural equations in DSGE models), and show that it is possible, under regularity conditions that are straightforward to check, to derive a problem with linear constraints and a quadratic objective that approximates the exact proble...

We used the fluorescence ubiquitination-based cell cycle indicator (FUCCI) to monitor cell cycle arrest after treatment of FUCCI-expressing HeLa cells (FUCCI-HeLa) with a traditional Chinese medicine (TCM) herbal mixture LQ, previously shown to have anti-tumor and anti-metastatic activity in mouse models. Paclitaxel was used as the positive control. In 2D monolayer culture, the untreated contro...